Problem: A cube with side length $w$ has a volume of $512$ cubic centimeters. The following equation shows the volume of the cube. $w^3 = 512$ What is the side length of the cube in centimeters?
Let's solve for $w$. Remember that it is not possible to have a negative side length! $ $ w 3 w 3 − − − √ 3 w = 512 = 512 − − − √ 3 = 8 \begin{aligned} w^3 &= 512\\ \\ \sqrt[\leftroot{-2}\uproot{2}\scriptstyle 3]{w^3} &= \sqrt[\leftroot{-2}\uproot{2}\scriptstyle 3]{512}\\ \\ w&= 8 \end{aligned} The side length of the cube is $8 \text{ cm}$.